Transcript CHAPTER 1: The Birth of Modern Physics

Physics 222: Modern Physics for Engineers
Fall 2013
Instructor: Hans Schuessler
Website: http://sibor.physics.tamu.edu
Office: 213B
Email: [email protected]
Course objectives: To learn the physics of the 20th century
Course outcomes: Know the basic laws of relativity, quantum and
atomic physics, nuclear physics ad solid state physics.
Text: Modern Physics for Scientists and Engineers
by S. Thornton and A. Rex, 4th Edition, ISBN: 9781133103721
CHAPTER 1
"The eternal mystery of the world is its comprehensibility.“
"Anyone who has never made a mistake has never tried
anything new."
A. Einstein
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1.1 Classical Physics of the 1890s
1.2 The Kinetic Theory of Gases
1.3 Waves and Particles
1.4 Conservation Laws and Fundamental Forces
1.5 The Atomic Theory of Matter
1.6 Unresolved Questions of 1895 and New Horizons
1.1: Classical Physics of the 1890s
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Mechanics
Electromagnetism
Thermodynamics
MECHANICS
CLASSICAL
PHYSICS
1.1
ELECTRICITY
AND
MAGNETISM
THERMODYNAMICS
CONSERVATION LAWS
Triumph of Classical Physics:
The Conservation Laws
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Conservation of energy: The total sum of
energy (in all its forms) is conserved in all
interactions.
Conservation of linear momentum: In the
absence of external forces, linear momentum is
conserved in all interactions.
Conservation of angular momentum: In the
absence of external torque, angular momentum is
conserved in all interactions.
Conservation of charge: Electric charge is
conserved in all interactions.
Mechanics
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Galileo Galilei (1564-1642)
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Great experimentalist
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Principle of inertia
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Established experimental foundations
Kinematics equations for constant
acceleration
v  v 0  at
General formulas:
1 2
x  x0  v0t  at
2
v  dx / dt
2
a  dv / dt  d x / dt
2
v  v  2a( x  x0 )
2
2
0
v0  v
x  x0  (
)t
2
Testing Kinetics for a=9.80m/s2
1 2
y  at
2
All objects fall with the same constant acceleration!!
Isaac Newton (1642-1727)
Three laws describing the relationship between
mass and acceleration.
 Newton’s first law (law of inertia): An object in motion with a
constant velocity will continue in motion unless acted upon by some
net external force.
 Newton’s second law: Introduces force (F) as responsible for the
change in linear momentum (p):
 Newton’s third law (law of action and reaction): The force exerted
by body 1 on body 2 is equal in magnitude and opposite in direction
to the force that body 2 exerts on body 1.
Inertial Frames K and K’
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K is at rest and K’ is moving with velocity
Axes are parallel
K and K’ are said to be INERTIAL COORDINATE SYSTEMS
The Galilean Transformation
For a point P
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In system K: P = (x, y, z, t)
In system K’: P = (x’, y’, z’, t’)
P
x
vt
K
K’
x’-axis
x-axis
pulling a sled, Michelangelo’s assistant
For forward motion: FAG> FAS FSA > FSG
Gravitation
Newton’s Law of
Gravitation
Gm1m2
Fg 
r2
G=gravitational constant = 6.673(10) 10-11 Nm2 / kg 2
Note: The weight  of a body of mass m on the earth's surface with
radius R E is
GmE  m
  mg 
2
RE
GmE
or g  2
RE
Cavendish balance
Light source
(
)
Henry Cavendish(1798) announced that he has
weighted the earth.
M
a gr  g  G 2
R
Electromagnetism: 18th-19th centuries
Contributions made by:
 Coulomb (1736-1806)
 Oersted (1777-1851)
 Young (1773-1829)
 Ampère (1775-1836)
 Faraday (1791-1867)
 Henry (1797-1878)
 Maxwell (1831-1879)
 Hertz (1857-1894)
Culminates in Maxwell’s Equations
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Gauss’s law (ΦE):
(electric field)
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Gauss’s law (ΦB):
(magnetic field)
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Faraday’s law:
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Ampère’s law:
(Generalized)
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Lorentz law:
(force)
Gauss (1777 –1855)
Thermodynamics
Contributions made by:
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Benjamin Thompson (1753-1814) (frictional heat)
(Count Rumford)
Sadi Carnot (1796-1832) (heat engine and Carnot cycle)
James Joule (1818-1889) (mechanical equivalent of heat))
Rudolf Clausius (1822-1888) (heat can never pass from a
colder to a warmer body without some other change)
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William Thompson (1824-1907)
(Lord Kelvin) (proposed absolute temperature scale)
Primary Results
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Deals with temperature, heat, work, and the
internal energy of systems
Introduces thermal equilibrium
The first law establishes heat as energy and
expresses conservation of energy
Introduces the concept of internal energy and
considers temperature as a measure of
internal energy
Introduces limitations of the energy
processes that can or cannot take place
The Laws of Thermodynamics
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First law: The change in the internal energy ΔU of a
system is equal to the heat Q added to a system plus the
work W done on the system
ΔU = Q + W
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Second law: It is not possible to convert heat completely
into work without some other change taking place.
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The “zeroth” law: Two systems in thermal equilibrium with
a third system are in thermal equilibrium with each other.
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Third law: It is not possible to achieve an absolute zero
temperature.
1.2: The Kinetic Theory of Gases
Contributions made by:
 Robert Boyle (1627-1691)
 Jacques Charles (1746-1823)
 Joseph Louis Gay-Lussac (1778-1823)
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Culminates in the ideal gas equation for n
moles of a “simple” gas:
PV = nRT
(where R is the ideal gas constant, 8.31 J/(mol · K)
Additional Contributions
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Amedeo Avogadro (1776-1856) (number of
molecules in a mole and their weights)
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John Dalton (1766-1844) (atomic theory of elements)
Daniel Bernoulli (1700-1782) (kinetic theory of gases)
Ludwig Boltzmann (1844-1906) (kinetic theory of
gases, entropy as log() of probability)
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James Clerk Maxwell (1831-1879) (velocity
distribution)
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J. Willard Gibbs (1939-1903) (thermodynamic and
chemical potentials)
Primary Results
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Average molecular kinetic energy directly related to
absolute temperature
Internal energy U directly related to the average
molecular kinetic energy
Internal energy equally distributed among the
number of degrees of freedom (f ) of the system
containing n moles of substance
(NA = 6.022×1023 mol−1
Avogadro’s number: number of molecules in 1 mole)
Primary Results
1. The molar heat capacity (cV) is given by
R=8.31 J/(mol K)
Other Primary Results
2. Maxwell derives a relation for the molecular speed
distribution f (v):
3. Boltzmann contributes to determine the root-meansquare of the molecular speed
Thus relating energy to the temperature for an ideal gas
Molecular speeds in an ideal gas
1 2 3
Kav (molecule)  mvev
 kT
2
2
21
1.3: Waves and Particles
Two ways in which energy is transported:
1)
Point mass interaction: transfers of
momentum and kinetic energy: particles
2)
Extended regions wherein energy transfers
by way of vibrations and rotations are
observed: waves
Particles vs. Waves
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Two distinct phenomena describing physical
interactions
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Particles in the form of point masses and waves in
the form of perturbation in a mass distribution, i.e.,
a material medium
The distinctions are observationally quite clear;
however, not so for the case of visible light
Thus by the 17th century begins the major
disagreement concerning the nature of light
The Nature of Light
Contributions made by:
 Isaac Newton (1642-1742)
 Christian Huygens (1629 -1695)
 Thomas Young (1773 -1829)
 Augustin Fresnel (1788 – 1829)
The Nature of Light
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Newton suggested the corpuscular (particle)
theory
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Particles of light travel in straight lines or rays
Explained sharp shadows
Explained reflection and refraction
The Nature of Light
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Christian Huygens promoted the wave theory
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Light propagates as a wave of concentric circles
from the point of origin
Explained reflection and refraction
Did not explain sharp shadows
The Wave Theory Advances…
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Contributions by Huygens, Young, Fresnel
and Maxwell
Double-slit interference patterns
Refraction of light from a vacuum to a
medium
Light is an electromagnetic phenomenon
Establishes that light propagates as a wave
The Electromagnetic Spectrum
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Visible light covers only a small range of the total
electromagnetic spectrum
All electromagnetic waves travel in a vacuum with a
speed c given by:
(where μ0 and ε0 are the respective permeability and
permittivity of “free” space)
1.4: Conservation Laws and Fundamental
Forces
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Recall the fundamental conservation laws:
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Conservation of energy
Conservation of linear momentum
Conservation of angular momentum
Conservation of electric charge
Later we will establish the conservation of
mass as part of the conservation of energy
Modern Results
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In addition to the classical conservation laws,
two modern results will include:
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The conservation of baryons and leptons
The fundamental invariance principles for time
reversal, distance, and parity
Also in the Modern Context…
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The three fundamental forces are introduced
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Gravitational:
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Electroweak
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Weak: Responsible for nuclear beta decay and effective only
over distances of ~10−15 m
Electromagnetic:
(Coulomb force)
Strong: Responsible for “holding” the nucleus together
and effective less than ~10−15 m
Unification
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Neutrons and protons are composed of
quarks, which have the color force acting
between them
Grand Unified Theory (GUT) attempts to unify
electroweak and strong forces
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String theory is one of these
They have yet to be verified experimentally
Unification of Forces
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Maxwell unified the electric and magnetic
forces as fundamentally the same force; now
referred to as the electromagnetic force
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In the 1970’s Glashow, Weinberg, and
Salem proposed the equivalence of the
electromagnetic and the weak forces (at high
energy); now referred to as the electroweak
interaction
Goal: Unification of All Forces
into a Single Force
1.5: The Atomic Theory of Matter
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Initiated by Democritus and Leucippus (~450 B.C.)
(first to us the Greek atomos, meaning “indivisible”)
In addition to fundamental contributions by Boyle, Charles,
and Gay-Lussac, Proust (1754 – 1826) proposes the law of
definite proportions
Dalton advances the atomic theory of matter to explain
the law of definite proportions
Avogadro proposes that all gases at the same temperature,
pressure, and volume contain the same number of
molecules (atoms); viz. 6.02 × 1023 atoms per mole
Cannizzaro (1826 – 1910) makes the distinction between
atoms and molecules advancing the ideas of Avogadro.
Further Advances in Atomic Theory
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Maxwell derives the speed distribution of
atoms in a gas
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Robert Brown (1753 – 1858) observes
microscopic “random” motion of suspended
grains of pollen in water
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Einstein in the 20th century explains this
random motion using atomic theory
Opposition to the Theory
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Ernst Mach (1838 – 1916) opposes the
theory on the basis of logical positivism, i.e.,
atoms being “unseen” place into question
their reality
Wilhelm Ostwald (1853 – 1932) supports this
premise but on experimental results of
radioactivity, discrete spectral lines, and the
formation of molecular structures
Overwhelming Evidence for Existence of
Atoms
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Max Planck (1858 – 1947) advances the
concept to explain blackbody radiation by use
of submicroscopic “quanta”
Boltzmann requires existence of atoms for his
advances in statistical mechanics
Albert Einstein (1879 – 1955) uses molecules
to explain Brownian motion and determines
the approximate value of their size and mass
Jean Perrin (1870 – 1942) experimentally
verifies Einstein’s predictions
1.6: Unresolved Questions of 1895 and
New Horizons
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The atomic theory controversy raises
fundamental questions
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It was not universally accepted
The constitutes (if any) of atoms became a
significant question
The structure of matter remained unknown with
certainty
Further Complications
Three fundamental problems:
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The question of the existence of an
electromagnetic medium
The problem of observed differences in the
electric and magnetic field between stationary
and moving reference systems
The failure of classical physics to explain
blackbody radiation
Additional Discoveries Contribute to the
Complications
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Discovery of x-rays
Discovery of radioactivity
Discovery of the electron
Discovery of the Zeeman effect
The Beginnings of Modern Physics
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These new discoveries and the many
resulting complications required a revision of
the fundamental physical assumptions that
culminated in the huge successes of physics
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To this end, the introduction of the modern
theory of relativity and quantum mechanics
becomes the starting point of this most
fascinating revision.
Homework assignment:
Problems
2.1. #1,2
2.2. #4